Properties

Label 5472.2.a.bt.1.3
Level $5472$
Weight $2$
Character 5472.1
Self dual yes
Analytic conductor $43.694$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.6941399860\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.15317.1
Defining polynomial: \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 608)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.32973\) of defining polynomial
Character \(\chi\) \(=\) 5472.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.844614 q^{5} +5.06562 q^{7} +O(q^{10})\) \(q+0.844614 q^{5} +5.06562 q^{7} +2.84461 q^{11} +2.90210 q^{13} -7.72508 q^{17} -1.00000 q^{19} +3.91023 q^{23} -4.28663 q^{25} -2.90210 q^{29} +7.00814 q^{31} +4.27849 q^{35} +9.00814 q^{37} +6.81233 q^{41} -5.96772 q^{43} -1.04042 q^{47} +18.6605 q^{49} +9.03334 q^{53} +2.40260 q^{55} +0.749220 q^{59} +2.27849 q^{61} +2.45115 q^{65} -10.3739 q^{67} +2.13124 q^{71} +4.60197 q^{73} +14.4097 q^{77} -3.88503 q^{79} +8.44201 q^{83} -6.52470 q^{85} -16.0667 q^{89} +14.7009 q^{91} -0.844614 q^{95} -3.68923 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{5} + q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{5} + q^{7} + 7 q^{11} + 10 q^{13} - 5 q^{17} - 4 q^{19} - 8 q^{23} + 17 q^{25} - 10 q^{29} + 6 q^{31} + 5 q^{35} + 14 q^{37} + 2 q^{41} - 3 q^{43} - 3 q^{47} + 7 q^{49} - 4 q^{53} + 35 q^{55} + 20 q^{59} - 3 q^{61} + 12 q^{65} - 8 q^{67} - 30 q^{71} + 9 q^{73} + 7 q^{77} - 10 q^{79} + 4 q^{83} + 19 q^{85} + 16 q^{89} - 10 q^{91} + q^{95} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.844614 0.377723 0.188861 0.982004i \(-0.439520\pi\)
0.188861 + 0.982004i \(0.439520\pi\)
\(6\) 0 0
\(7\) 5.06562 1.91462 0.957312 0.289056i \(-0.0933412\pi\)
0.957312 + 0.289056i \(0.0933412\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.84461 0.857683 0.428842 0.903380i \(-0.358922\pi\)
0.428842 + 0.903380i \(0.358922\pi\)
\(12\) 0 0
\(13\) 2.90210 0.804897 0.402449 0.915443i \(-0.368159\pi\)
0.402449 + 0.915443i \(0.368159\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.72508 −1.87361 −0.936803 0.349857i \(-0.886230\pi\)
−0.936803 + 0.349857i \(0.886230\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.91023 0.815340 0.407670 0.913129i \(-0.366341\pi\)
0.407670 + 0.913129i \(0.366341\pi\)
\(24\) 0 0
\(25\) −4.28663 −0.857326
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.90210 −0.538906 −0.269453 0.963014i \(-0.586843\pi\)
−0.269453 + 0.963014i \(0.586843\pi\)
\(30\) 0 0
\(31\) 7.00814 1.25870 0.629349 0.777123i \(-0.283322\pi\)
0.629349 + 0.777123i \(0.283322\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.27849 0.723197
\(36\) 0 0
\(37\) 9.00814 1.48093 0.740464 0.672096i \(-0.234606\pi\)
0.740464 + 0.672096i \(0.234606\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.81233 1.06391 0.531954 0.846773i \(-0.321458\pi\)
0.531954 + 0.846773i \(0.321458\pi\)
\(42\) 0 0
\(43\) −5.96772 −0.910069 −0.455034 0.890474i \(-0.650373\pi\)
−0.455034 + 0.890474i \(0.650373\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.04042 −0.151760 −0.0758802 0.997117i \(-0.524177\pi\)
−0.0758802 + 0.997117i \(0.524177\pi\)
\(48\) 0 0
\(49\) 18.6605 2.66579
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.03334 1.24082 0.620412 0.784276i \(-0.286965\pi\)
0.620412 + 0.784276i \(0.286965\pi\)
\(54\) 0 0
\(55\) 2.40260 0.323966
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.749220 0.0975401 0.0487701 0.998810i \(-0.484470\pi\)
0.0487701 + 0.998810i \(0.484470\pi\)
\(60\) 0 0
\(61\) 2.27849 0.291731 0.145866 0.989304i \(-0.453403\pi\)
0.145866 + 0.989304i \(0.453403\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.45115 0.304028
\(66\) 0 0
\(67\) −10.3739 −1.26737 −0.633686 0.773590i \(-0.718459\pi\)
−0.633686 + 0.773590i \(0.718459\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.13124 0.252932 0.126466 0.991971i \(-0.459637\pi\)
0.126466 + 0.991971i \(0.459637\pi\)
\(72\) 0 0
\(73\) 4.60197 0.538620 0.269310 0.963054i \(-0.413204\pi\)
0.269310 + 0.963054i \(0.413204\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 14.4097 1.64214
\(78\) 0 0
\(79\) −3.88503 −0.437100 −0.218550 0.975826i \(-0.570133\pi\)
−0.218550 + 0.975826i \(0.570133\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.44201 0.926631 0.463316 0.886193i \(-0.346660\pi\)
0.463316 + 0.886193i \(0.346660\pi\)
\(84\) 0 0
\(85\) −6.52470 −0.707703
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −16.0667 −1.70306 −0.851532 0.524302i \(-0.824326\pi\)
−0.851532 + 0.524302i \(0.824326\pi\)
\(90\) 0 0
\(91\) 14.7009 1.54108
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.844614 −0.0866555
\(96\) 0 0
\(97\) −3.68923 −0.374584 −0.187292 0.982304i \(-0.559971\pi\)
−0.187292 + 0.982304i \(0.559971\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 16.2462 1.61656 0.808279 0.588799i \(-0.200399\pi\)
0.808279 + 0.588799i \(0.200399\pi\)
\(102\) 0 0
\(103\) 0.812333 0.0800415 0.0400208 0.999199i \(-0.487258\pi\)
0.0400208 + 0.999199i \(0.487258\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.88860 0.955967 0.477983 0.878369i \(-0.341368\pi\)
0.477983 + 0.878369i \(0.341368\pi\)
\(108\) 0 0
\(109\) −10.8375 −1.03805 −0.519024 0.854760i \(-0.673704\pi\)
−0.519024 + 0.854760i \(0.673704\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.310773 0.0292351 0.0146175 0.999893i \(-0.495347\pi\)
0.0146175 + 0.999893i \(0.495347\pi\)
\(114\) 0 0
\(115\) 3.30264 0.307972
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −39.1323 −3.58725
\(120\) 0 0
\(121\) −2.90817 −0.264379
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.84361 −0.701554
\(126\) 0 0
\(127\) −18.6882 −1.65831 −0.829156 0.559017i \(-0.811178\pi\)
−0.829156 + 0.559017i \(0.811178\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −16.6055 −1.45083 −0.725416 0.688310i \(-0.758353\pi\)
−0.725416 + 0.688310i \(0.758353\pi\)
\(132\) 0 0
\(133\) −5.06562 −0.439245
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.91274 0.248852 0.124426 0.992229i \(-0.460291\pi\)
0.124426 + 0.992229i \(0.460291\pi\)
\(138\) 0 0
\(139\) 0.278492 0.0236214 0.0118107 0.999930i \(-0.496240\pi\)
0.0118107 + 0.999930i \(0.496240\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.25535 0.690347
\(144\) 0 0
\(145\) −2.45115 −0.203557
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.08269 0.662160 0.331080 0.943603i \(-0.392587\pi\)
0.331080 + 0.943603i \(0.392587\pi\)
\(150\) 0 0
\(151\) −15.0585 −1.22545 −0.612723 0.790297i \(-0.709926\pi\)
−0.612723 + 0.790297i \(0.709926\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.91917 0.475439
\(156\) 0 0
\(157\) 10.9273 0.872094 0.436047 0.899924i \(-0.356378\pi\)
0.436047 + 0.899924i \(0.356378\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 19.8078 1.56107
\(162\) 0 0
\(163\) −0.697363 −0.0546217 −0.0273108 0.999627i \(-0.508694\pi\)
−0.0273108 + 0.999627i \(0.508694\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.24621 0.483346 0.241673 0.970358i \(-0.422304\pi\)
0.241673 + 0.970358i \(0.422304\pi\)
\(168\) 0 0
\(169\) −4.57782 −0.352140
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.69736 −0.509191 −0.254596 0.967048i \(-0.581942\pi\)
−0.254596 + 0.967048i \(0.581942\pi\)
\(174\) 0 0
\(175\) −21.7144 −1.64146
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.2462 1.36379 0.681893 0.731452i \(-0.261157\pi\)
0.681893 + 0.731452i \(0.261157\pi\)
\(180\) 0 0
\(181\) 17.5651 1.30561 0.652803 0.757528i \(-0.273593\pi\)
0.652803 + 0.757528i \(0.273593\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.60839 0.559380
\(186\) 0 0
\(187\) −21.9749 −1.60696
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.19686 0.520747 0.260373 0.965508i \(-0.416154\pi\)
0.260373 + 0.965508i \(0.416154\pi\)
\(192\) 0 0
\(193\) −2.92730 −0.210712 −0.105356 0.994435i \(-0.533598\pi\)
−0.105356 + 0.994435i \(0.533598\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.1394 0.793648 0.396824 0.917895i \(-0.370112\pi\)
0.396824 + 0.917895i \(0.370112\pi\)
\(198\) 0 0
\(199\) −5.57220 −0.395003 −0.197501 0.980303i \(-0.563283\pi\)
−0.197501 + 0.980303i \(0.563283\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −14.7009 −1.03180
\(204\) 0 0
\(205\) 5.75379 0.401862
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.84461 −0.196766
\(210\) 0 0
\(211\) 1.23451 0.0849871 0.0424935 0.999097i \(-0.486470\pi\)
0.0424935 + 0.999097i \(0.486470\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.04042 −0.343754
\(216\) 0 0
\(217\) 35.5006 2.40993
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −22.4189 −1.50806
\(222\) 0 0
\(223\) 5.76092 0.385780 0.192890 0.981220i \(-0.438214\pi\)
0.192890 + 0.981220i \(0.438214\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.1862 −0.742455 −0.371228 0.928542i \(-0.621063\pi\)
−0.371228 + 0.928542i \(0.621063\pi\)
\(228\) 0 0
\(229\) 25.3624 1.67600 0.837999 0.545672i \(-0.183726\pi\)
0.837999 + 0.545672i \(0.183726\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.33804 −0.546243 −0.273122 0.961980i \(-0.588056\pi\)
−0.273122 + 0.961980i \(0.588056\pi\)
\(234\) 0 0
\(235\) −0.878750 −0.0573233
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.4441 −1.06368 −0.531839 0.846845i \(-0.678499\pi\)
−0.531839 + 0.846845i \(0.678499\pi\)
\(240\) 0 0
\(241\) −12.8286 −0.826363 −0.413182 0.910649i \(-0.635583\pi\)
−0.413182 + 0.910649i \(0.635583\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.7609 1.00693
\(246\) 0 0
\(247\) −2.90210 −0.184656
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 17.8527 1.12686 0.563428 0.826165i \(-0.309482\pi\)
0.563428 + 0.826165i \(0.309482\pi\)
\(252\) 0 0
\(253\) 11.1231 0.699304
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.49342 −0.0931572 −0.0465786 0.998915i \(-0.514832\pi\)
−0.0465786 + 0.998915i \(0.514832\pi\)
\(258\) 0 0
\(259\) 45.6318 2.83542
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.483433 0.0298097 0.0149049 0.999889i \(-0.495255\pi\)
0.0149049 + 0.999889i \(0.495255\pi\)
\(264\) 0 0
\(265\) 7.62968 0.468688
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8.45115 −0.515276 −0.257638 0.966242i \(-0.582944\pi\)
−0.257638 + 0.966242i \(0.582944\pi\)
\(270\) 0 0
\(271\) 16.5822 1.00730 0.503648 0.863909i \(-0.331991\pi\)
0.503648 + 0.863909i \(0.331991\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12.1938 −0.735314
\(276\) 0 0
\(277\) 15.7124 0.944065 0.472032 0.881581i \(-0.343521\pi\)
0.472032 + 0.881581i \(0.343521\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.13938 −0.187280 −0.0936398 0.995606i \(-0.529850\pi\)
−0.0936398 + 0.995606i \(0.529850\pi\)
\(282\) 0 0
\(283\) 26.3884 1.56863 0.784315 0.620363i \(-0.213015\pi\)
0.784315 + 0.620363i \(0.213015\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 34.5087 2.03698
\(288\) 0 0
\(289\) 42.6768 2.51040
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −13.5903 −0.793955 −0.396978 0.917828i \(-0.629941\pi\)
−0.396978 + 0.917828i \(0.629941\pi\)
\(294\) 0 0
\(295\) 0.632801 0.0368431
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 11.3479 0.656265
\(300\) 0 0
\(301\) −30.2302 −1.74244
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.92445 0.110193
\(306\) 0 0
\(307\) 3.44302 0.196503 0.0982516 0.995162i \(-0.468675\pi\)
0.0982516 + 0.995162i \(0.468675\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −29.4935 −1.67242 −0.836211 0.548408i \(-0.815234\pi\)
−0.836211 + 0.548408i \(0.815234\pi\)
\(312\) 0 0
\(313\) −10.0631 −0.568801 −0.284400 0.958706i \(-0.591794\pi\)
−0.284400 + 0.958706i \(0.591794\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.14931 −0.233049 −0.116524 0.993188i \(-0.537175\pi\)
−0.116524 + 0.993188i \(0.537175\pi\)
\(318\) 0 0
\(319\) −8.25535 −0.462211
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.72508 0.429835
\(324\) 0 0
\(325\) −12.4402 −0.690059
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.27036 −0.290564
\(330\) 0 0
\(331\) −25.8886 −1.42297 −0.711483 0.702703i \(-0.751976\pi\)
−0.711483 + 0.702703i \(0.751976\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.76192 −0.478715
\(336\) 0 0
\(337\) 31.5097 1.71644 0.858221 0.513280i \(-0.171570\pi\)
0.858221 + 0.513280i \(0.171570\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 19.9354 1.07956
\(342\) 0 0
\(343\) 59.0677 3.18936
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.9173 −0.747120 −0.373560 0.927606i \(-0.621863\pi\)
−0.373560 + 0.927606i \(0.621863\pi\)
\(348\) 0 0
\(349\) 6.34305 0.339536 0.169768 0.985484i \(-0.445698\pi\)
0.169768 + 0.985484i \(0.445698\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 32.0794 1.70741 0.853707 0.520754i \(-0.174349\pi\)
0.853707 + 0.520754i \(0.174349\pi\)
\(354\) 0 0
\(355\) 1.80008 0.0955381
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.86670 −0.0985205 −0.0492603 0.998786i \(-0.515686\pi\)
−0.0492603 + 0.998786i \(0.515686\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.88689 0.203449
\(366\) 0 0
\(367\) −20.8840 −1.09014 −0.545069 0.838391i \(-0.683496\pi\)
−0.545069 + 0.838391i \(0.683496\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 45.7595 2.37571
\(372\) 0 0
\(373\) 25.9819 1.34529 0.672647 0.739964i \(-0.265157\pi\)
0.672647 + 0.739964i \(0.265157\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.42218 −0.433764
\(378\) 0 0
\(379\) −2.50301 −0.128571 −0.0642855 0.997932i \(-0.520477\pi\)
−0.0642855 + 0.997932i \(0.520477\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −21.8155 −1.11472 −0.557359 0.830272i \(-0.688185\pi\)
−0.557359 + 0.830272i \(0.688185\pi\)
\(384\) 0 0
\(385\) 12.1707 0.620274
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −35.2383 −1.78665 −0.893327 0.449407i \(-0.851635\pi\)
−0.893327 + 0.449407i \(0.851635\pi\)
\(390\) 0 0
\(391\) −30.2069 −1.52763
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.28135 −0.165103
\(396\) 0 0
\(397\) −27.0263 −1.35641 −0.678205 0.734873i \(-0.737242\pi\)
−0.678205 + 0.734873i \(0.737242\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 24.8932 1.24311 0.621553 0.783372i \(-0.286502\pi\)
0.621553 + 0.783372i \(0.286502\pi\)
\(402\) 0 0
\(403\) 20.3383 1.01312
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 25.6247 1.27017
\(408\) 0 0
\(409\) −14.8336 −0.733475 −0.366738 0.930324i \(-0.619525\pi\)
−0.366738 + 0.930324i \(0.619525\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.79526 0.186753
\(414\) 0 0
\(415\) 7.13024 0.350010
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.05955 −0.296028 −0.148014 0.988985i \(-0.547288\pi\)
−0.148014 + 0.988985i \(0.547288\pi\)
\(420\) 0 0
\(421\) 13.8670 0.675834 0.337917 0.941176i \(-0.390278\pi\)
0.337917 + 0.941176i \(0.390278\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 33.1145 1.60629
\(426\) 0 0
\(427\) 11.5420 0.558555
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −11.5580 −0.556729 −0.278364 0.960476i \(-0.589792\pi\)
−0.278364 + 0.960476i \(0.589792\pi\)
\(432\) 0 0
\(433\) −31.7468 −1.52565 −0.762826 0.646604i \(-0.776189\pi\)
−0.762826 + 0.646604i \(0.776189\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.91023 −0.187052
\(438\) 0 0
\(439\) 24.8840 1.18765 0.593825 0.804594i \(-0.297617\pi\)
0.593825 + 0.804594i \(0.297617\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −23.9911 −1.13985 −0.569926 0.821696i \(-0.693028\pi\)
−0.569926 + 0.821696i \(0.693028\pi\)
\(444\) 0 0
\(445\) −13.5701 −0.643286
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −32.1384 −1.51670 −0.758352 0.651845i \(-0.773995\pi\)
−0.758352 + 0.651845i \(0.773995\pi\)
\(450\) 0 0
\(451\) 19.3785 0.912496
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 12.4166 0.582099
\(456\) 0 0
\(457\) 29.1590 1.36400 0.681999 0.731353i \(-0.261111\pi\)
0.681999 + 0.731353i \(0.261111\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −18.6559 −0.868894 −0.434447 0.900697i \(-0.643056\pi\)
−0.434447 + 0.900697i \(0.643056\pi\)
\(462\) 0 0
\(463\) −22.6005 −1.05034 −0.525168 0.850999i \(-0.675997\pi\)
−0.525168 + 0.850999i \(0.675997\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.1666 −0.794377 −0.397189 0.917737i \(-0.630014\pi\)
−0.397189 + 0.917737i \(0.630014\pi\)
\(468\) 0 0
\(469\) −52.5502 −2.42654
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −16.9759 −0.780551
\(474\) 0 0
\(475\) 4.28663 0.196684
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16.2625 −0.743052 −0.371526 0.928423i \(-0.621165\pi\)
−0.371526 + 0.928423i \(0.621165\pi\)
\(480\) 0 0
\(481\) 26.1425 1.19200
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.11597 −0.141489
\(486\) 0 0
\(487\) −18.2071 −0.825041 −0.412520 0.910948i \(-0.635351\pi\)
−0.412520 + 0.910948i \(0.635351\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 39.2493 1.77130 0.885649 0.464356i \(-0.153714\pi\)
0.885649 + 0.464356i \(0.153714\pi\)
\(492\) 0 0
\(493\) 22.4189 1.00970
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.7961 0.484270
\(498\) 0 0
\(499\) 35.7541 1.60057 0.800286 0.599619i \(-0.204681\pi\)
0.800286 + 0.599619i \(0.204681\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.5512 1.22845 0.614223 0.789132i \(-0.289470\pi\)
0.614223 + 0.789132i \(0.289470\pi\)
\(504\) 0 0
\(505\) 13.7218 0.610611
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.6328 0.648588 0.324294 0.945956i \(-0.394873\pi\)
0.324294 + 0.945956i \(0.394873\pi\)
\(510\) 0 0
\(511\) 23.3118 1.03125
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.686107 0.0302335
\(516\) 0 0
\(517\) −2.95958 −0.130162
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.59926 0.332929 0.166465 0.986047i \(-0.446765\pi\)
0.166465 + 0.986047i \(0.446765\pi\)
\(522\) 0 0
\(523\) −19.8723 −0.868956 −0.434478 0.900682i \(-0.643067\pi\)
−0.434478 + 0.900682i \(0.643067\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −54.1384 −2.35830
\(528\) 0 0
\(529\) −7.71007 −0.335220
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 19.7701 0.856336
\(534\) 0 0
\(535\) 8.35204 0.361090
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 53.0820 2.28640
\(540\) 0 0
\(541\) 27.6982 1.19084 0.595420 0.803415i \(-0.296986\pi\)
0.595420 + 0.803415i \(0.296986\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −9.15353 −0.392094
\(546\) 0 0
\(547\) −33.8871 −1.44891 −0.724455 0.689322i \(-0.757908\pi\)
−0.724455 + 0.689322i \(0.757908\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.90210 0.123634
\(552\) 0 0
\(553\) −19.6801 −0.836883
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.28763 0.351158 0.175579 0.984465i \(-0.443820\pi\)
0.175579 + 0.984465i \(0.443820\pi\)
\(558\) 0 0
\(559\) −17.3189 −0.732512
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.11397 −0.215528 −0.107764 0.994177i \(-0.534369\pi\)
−0.107764 + 0.994177i \(0.534369\pi\)
\(564\) 0 0
\(565\) 0.262483 0.0110427
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.92830 −0.0808387 −0.0404194 0.999183i \(-0.512869\pi\)
−0.0404194 + 0.999183i \(0.512869\pi\)
\(570\) 0 0
\(571\) 23.3785 0.978358 0.489179 0.872183i \(-0.337297\pi\)
0.489179 + 0.872183i \(0.337297\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −16.7617 −0.699012
\(576\) 0 0
\(577\) −26.8807 −1.11906 −0.559530 0.828810i \(-0.689018\pi\)
−0.559530 + 0.828810i \(0.689018\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 42.7640 1.77415
\(582\) 0 0
\(583\) 25.6964 1.06423
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −36.7922 −1.51858 −0.759288 0.650754i \(-0.774453\pi\)
−0.759288 + 0.650754i \(0.774453\pi\)
\(588\) 0 0
\(589\) −7.00814 −0.288765
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 33.9034 1.39225 0.696123 0.717922i \(-0.254907\pi\)
0.696123 + 0.717922i \(0.254907\pi\)
\(594\) 0 0
\(595\) −33.0517 −1.35499
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.06456 −0.166073 −0.0830367 0.996546i \(-0.526462\pi\)
−0.0830367 + 0.996546i \(0.526462\pi\)
\(600\) 0 0
\(601\) −27.5560 −1.12403 −0.562016 0.827126i \(-0.689974\pi\)
−0.562016 + 0.827126i \(0.689974\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.45628 −0.0998621
\(606\) 0 0
\(607\) −25.5743 −1.03803 −0.519014 0.854766i \(-0.673701\pi\)
−0.519014 + 0.854766i \(0.673701\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.01939 −0.122152
\(612\) 0 0
\(613\) −31.2383 −1.26170 −0.630852 0.775903i \(-0.717295\pi\)
−0.630852 + 0.775903i \(0.717295\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.86189 0.235991 0.117995 0.993014i \(-0.462353\pi\)
0.117995 + 0.993014i \(0.462353\pi\)
\(618\) 0 0
\(619\) 31.6481 1.27204 0.636022 0.771671i \(-0.280579\pi\)
0.636022 + 0.771671i \(0.280579\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −81.3877 −3.26073
\(624\) 0 0
\(625\) 14.8083 0.592333
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −69.5885 −2.77468
\(630\) 0 0
\(631\) 3.86189 0.153739 0.0768696 0.997041i \(-0.475507\pi\)
0.0768696 + 0.997041i \(0.475507\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15.7843 −0.626382
\(636\) 0 0
\(637\) 54.1546 2.14569
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 14.9919 0.592143 0.296072 0.955166i \(-0.404323\pi\)
0.296072 + 0.955166i \(0.404323\pi\)
\(642\) 0 0
\(643\) 12.4906 0.492580 0.246290 0.969196i \(-0.420788\pi\)
0.246290 + 0.969196i \(0.420788\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.5743 −0.926802 −0.463401 0.886149i \(-0.653371\pi\)
−0.463401 + 0.886149i \(0.653371\pi\)
\(648\) 0 0
\(649\) 2.13124 0.0836585
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30.4693 −1.19236 −0.596178 0.802853i \(-0.703315\pi\)
−0.596178 + 0.802853i \(0.703315\pi\)
\(654\) 0 0
\(655\) −14.0253 −0.548012
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 39.9049 1.55447 0.777237 0.629209i \(-0.216621\pi\)
0.777237 + 0.629209i \(0.216621\pi\)
\(660\) 0 0
\(661\) −22.8156 −0.887422 −0.443711 0.896170i \(-0.646338\pi\)
−0.443711 + 0.896170i \(0.646338\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.27849 −0.165913
\(666\) 0 0
\(667\) −11.3479 −0.439392
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.48143 0.250213
\(672\) 0 0
\(673\) −37.0265 −1.42727 −0.713634 0.700519i \(-0.752952\pi\)
−0.713634 + 0.700519i \(0.752952\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 45.6733 1.75537 0.877683 0.479241i \(-0.159088\pi\)
0.877683 + 0.479241i \(0.159088\pi\)
\(678\) 0 0
\(679\) −18.6882 −0.717188
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13.9837 0.535072 0.267536 0.963548i \(-0.413790\pi\)
0.267536 + 0.963548i \(0.413790\pi\)
\(684\) 0 0
\(685\) 2.46014 0.0939972
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 26.2156 0.998736
\(690\) 0 0
\(691\) 0.00185566 7.05926e−5 0 3.52963e−5 1.00000i \(-0.499989\pi\)
3.52963e−5 1.00000i \(0.499989\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.235218 0.00892233
\(696\) 0 0
\(697\) −52.6258 −1.99334
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.0071 0.831198 0.415599 0.909548i \(-0.363572\pi\)
0.415599 + 0.909548i \(0.363572\pi\)
\(702\) 0 0
\(703\) −9.00814 −0.339748
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 82.2971 3.09510
\(708\) 0 0
\(709\) 3.94045 0.147987 0.0739934 0.997259i \(-0.476426\pi\)
0.0739934 + 0.997259i \(0.476426\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 27.4035 1.02627
\(714\) 0 0
\(715\) 6.97258 0.260760
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −29.0656 −1.08396 −0.541982 0.840390i \(-0.682326\pi\)
−0.541982 + 0.840390i \(0.682326\pi\)
\(720\) 0 0
\(721\) 4.11497 0.153249
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.4402 0.462018
\(726\) 0 0
\(727\) −10.1617 −0.376877 −0.188439 0.982085i \(-0.560343\pi\)
−0.188439 + 0.982085i \(0.560343\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 46.1011 1.70511
\(732\) 0 0
\(733\) 51.4777 1.90137 0.950686 0.310156i \(-0.100381\pi\)
0.950686 + 0.310156i \(0.100381\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −29.5097 −1.08700
\(738\) 0 0
\(739\) −33.1412 −1.21912 −0.609560 0.792740i \(-0.708654\pi\)
−0.609560 + 0.792740i \(0.708654\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 35.5006 1.30239 0.651195 0.758911i \(-0.274268\pi\)
0.651195 + 0.758911i \(0.274268\pi\)
\(744\) 0 0
\(745\) 6.82675 0.250113
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 50.0919 1.83032
\(750\) 0 0
\(751\) −15.2594 −0.556822 −0.278411 0.960462i \(-0.589808\pi\)
−0.278411 + 0.960462i \(0.589808\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.7187 −0.462879
\(756\) 0 0
\(757\) 7.28161 0.264655 0.132327 0.991206i \(-0.457755\pi\)
0.132327 + 0.991206i \(0.457755\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.47886 −0.343609 −0.171804 0.985131i \(-0.554960\pi\)
−0.171804 + 0.985131i \(0.554960\pi\)
\(762\) 0 0
\(763\) −54.8989 −1.98747
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.17431 0.0785098
\(768\) 0 0
\(769\) 19.2760 0.695112 0.347556 0.937659i \(-0.387012\pi\)
0.347556 + 0.937659i \(0.387012\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.19501 −0.330721 −0.165361 0.986233i \(-0.552879\pi\)
−0.165361 + 0.986233i \(0.552879\pi\)
\(774\) 0 0
\(775\) −30.0413 −1.07911
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.81233 −0.244077
\(780\) 0 0
\(781\) 6.06256 0.216935
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9.22935 0.329410
\(786\) 0 0
\(787\) −12.6847 −0.452159 −0.226080 0.974109i \(-0.572591\pi\)
−0.226080 + 0.974109i \(0.572591\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.57426 0.0559741
\(792\) 0 0
\(793\) 6.61241 0.234814
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27.4591 −0.972651 −0.486325 0.873778i \(-0.661663\pi\)
−0.486325 + 0.873778i \(0.661663\pi\)
\(798\) 0 0
\(799\) 8.03730 0.284339
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 13.0908 0.461965
\(804\) 0 0
\(805\) 16.7299 0.589652
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −18.2912 −0.643084 −0.321542 0.946895i \(-0.604201\pi\)
−0.321542 + 0.946895i \(0.604201\pi\)
\(810\) 0 0
\(811\) −6.28391 −0.220658 −0.110329 0.993895i \(-0.535190\pi\)
−0.110329 + 0.993895i \(0.535190\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −0.589002 −0.0206318
\(816\) 0 0
\(817\) 5.96772 0.208784
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 43.9103 1.53248 0.766240 0.642555i \(-0.222125\pi\)
0.766240 + 0.642555i \(0.222125\pi\)
\(822\) 0 0
\(823\) 26.2483 0.914957 0.457479 0.889221i \(-0.348753\pi\)
0.457479 + 0.889221i \(0.348753\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34.7726 −1.20916 −0.604581 0.796543i \(-0.706660\pi\)
−0.604581 + 0.796543i \(0.706660\pi\)
\(828\) 0 0
\(829\) −20.9184 −0.726525 −0.363263 0.931687i \(-0.618337\pi\)
−0.363263 + 0.931687i \(0.618337\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −144.154 −4.99464
\(834\) 0 0
\(835\) 5.27563 0.182571
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 41.0061 1.41569 0.707844 0.706368i \(-0.249668\pi\)
0.707844 + 0.706368i \(0.249668\pi\)
\(840\) 0 0
\(841\) −20.5778 −0.709580
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.86649 −0.133011
\(846\) 0 0
\(847\) −14.7317 −0.506187
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 35.2239 1.20746
\(852\) 0 0
\(853\) 11.5056 0.393943 0.196972 0.980409i \(-0.436889\pi\)
0.196972 + 0.980409i \(0.436889\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −14.7478 −0.503774 −0.251887 0.967757i \(-0.581051\pi\)
−0.251887 + 0.967757i \(0.581051\pi\)
\(858\) 0 0
\(859\) −36.3402 −1.23991 −0.619955 0.784637i \(-0.712849\pi\)
−0.619955 + 0.784637i \(0.712849\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 48.3454 1.64570 0.822849 0.568260i \(-0.192383\pi\)
0.822849 + 0.568260i \(0.192383\pi\)
\(864\) 0 0
\(865\) −5.65668 −0.192333
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −11.0514 −0.374893
\(870\) 0 0
\(871\) −30.1060 −1.02010
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −39.7328 −1.34321
\(876\) 0 0
\(877\) −4.23226 −0.142913 −0.0714567 0.997444i \(-0.522765\pi\)
−0.0714567 + 0.997444i \(0.522765\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −32.6651 −1.10051 −0.550257 0.834995i \(-0.685470\pi\)
−0.550257 + 0.834995i \(0.685470\pi\)
\(882\) 0 0
\(883\) 45.3320 1.52554 0.762772 0.646668i \(-0.223838\pi\)
0.762772 + 0.646668i \(0.223838\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −50.5271 −1.69653 −0.848267 0.529569i \(-0.822354\pi\)
−0.848267 + 0.529569i \(0.822354\pi\)
\(888\) 0 0
\(889\) −94.6675 −3.17504
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.04042 0.0348162
\(894\) 0 0
\(895\) 15.4110 0.515133
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −20.3383 −0.678320
\(900\) 0 0
\(901\) −69.7832 −2.32482
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.8357 0.493157
\(906\) 0 0
\(907\) 21.9823 0.729910 0.364955 0.931025i \(-0.381084\pi\)
0.364955 + 0.931025i \(0.381084\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −29.9950 −0.993778 −0.496889 0.867814i \(-0.665524\pi\)
−0.496889 + 0.867814i \(0.665524\pi\)
\(912\) 0 0
\(913\) 24.0143 0.794756
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −84.1174 −2.77780
\(918\) 0 0
\(919\) 30.5481 1.00769 0.503844 0.863795i \(-0.331919\pi\)
0.503844 + 0.863795i \(0.331919\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 6.18507 0.203584
\(924\) 0 0
\(925\) −38.6145 −1.26964
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 5.67151 0.186076 0.0930380 0.995663i \(-0.470342\pi\)
0.0930380 + 0.995663i \(0.470342\pi\)
\(930\) 0 0
\(931\) −18.6605 −0.611574
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −18.5603 −0.606985
\(936\) 0 0
\(937\) 33.6051 1.09783 0.548915 0.835878i \(-0.315041\pi\)
0.548915 + 0.835878i \(0.315041\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −30.0543 −0.979743 −0.489871 0.871795i \(-0.662956\pi\)
−0.489871 + 0.871795i \(0.662956\pi\)
\(942\) 0 0
\(943\) 26.6378 0.867447
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12.3058 −0.399883 −0.199942 0.979808i \(-0.564075\pi\)
−0.199942 + 0.979808i \(0.564075\pi\)
\(948\) 0 0
\(949\) 13.3554 0.433534
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −30.4674 −0.986937 −0.493468 0.869764i \(-0.664271\pi\)
−0.493468 + 0.869764i \(0.664271\pi\)
\(954\) 0 0
\(955\) 6.07857 0.196698
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 14.7548 0.476459
\(960\) 0 0
\(961\) 18.1140 0.584322
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.47244 −0.0795906
\(966\) 0 0
\(967\) 5.26560 0.169330 0.0846652 0.996409i \(-0.473018\pi\)
0.0846652 + 0.996409i \(0.473018\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −54.7895 −1.75828 −0.879139 0.476566i \(-0.841881\pi\)
−0.879139 + 0.476566i \(0.841881\pi\)
\(972\) 0 0
\(973\) 1.41074 0.0452261
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −28.9690 −0.926800 −0.463400 0.886149i \(-0.653371\pi\)
−0.463400 + 0.886149i \(0.653371\pi\)
\(978\) 0 0
\(979\) −45.7035 −1.46069
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 35.2997 1.12589 0.562943 0.826495i \(-0.309669\pi\)
0.562943 + 0.826495i \(0.309669\pi\)
\(984\) 0 0
\(985\) 9.40847 0.299779
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −23.3352 −0.742016
\(990\) 0 0
\(991\) 8.34833 0.265194 0.132597 0.991170i \(-0.457668\pi\)
0.132597 + 0.991170i \(0.457668\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.70635 −0.149201
\(996\) 0 0
\(997\) 5.81519 0.184169 0.0920845 0.995751i \(-0.470647\pi\)
0.0920845 + 0.995751i \(0.470647\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5472.2.a.bt.1.3 4
3.2 odd 2 608.2.a.i.1.3 4
4.3 odd 2 5472.2.a.bs.1.3 4
12.11 even 2 608.2.a.j.1.1 yes 4
24.5 odd 2 1216.2.a.x.1.2 4
24.11 even 2 1216.2.a.w.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
608.2.a.i.1.3 4 3.2 odd 2
608.2.a.j.1.1 yes 4 12.11 even 2
1216.2.a.w.1.4 4 24.11 even 2
1216.2.a.x.1.2 4 24.5 odd 2
5472.2.a.bs.1.3 4 4.3 odd 2
5472.2.a.bt.1.3 4 1.1 even 1 trivial